Bond numbers

Computation. Decide on an appropriate input matr ix of bond numbers... 

NONSTANDARD VALENCE STATES OF HETEROATOMS BONDING NUMBER (A CONVENTION)... 

Two general types of heterocyclic cations may be recognized those in which the charge results from an increase in the bonding number of an atom by the addition of a proton (or equivalent), and those in which the charge results from a decrease in the bonding number by removal of hydride. These two possibilities are shown for pyrrole in (167) and (168). 

Heterocyclic cations in which the bonding number is increased by a process other than the addition of a proton (or equivalent) present a special situation. Structures of this type usually result from the participation of an originally nonbonding electron pair or a heteroatom in the formation of a ring or a multiple bond. 

Meanwhile, the A convention combined with replacement nomenclature may be used to indicate the changed bonding number of the anionic site, and the suffix -ide appended, as shown in (202) and (203). Proposals for an anionic replacement prefix, analogous to the cationic -onia prefixes, are under consideration. 

In a complex such as the sulfate ion the sulfuiMjxygen bond assumes multiple-bond character through resonance involving one sigma bond and two pi bonds. An empirical equation has been formulated connecting interatomic distances and bond number for resonance of this sort. On application of this equation it is found that in many complexes the amounts of multiple-bond character are such as to cause all atoms to conform rather closely to the principle of electroneutrality. 

To make a calculation for three double bonds we need three more orbitals. These may be the three equatorial bonds of the trigonal prism with three caps that is, with 6 = 90° and = 60°, 180°, and 300° (the three other orbitals have 9 = 43.47° and 0 = 0°, 120°, and 240°). The axis for each of the three double bonds is placed midway between an equatorial orbital and one of the other orbitals. The double-bond axes lie at 6 = 63.73°, which corresponds to 101.85° for the bond angle for doubly bonded carbonyls in the M(CO)3 group (bond number n = 2). 

FlO. 1. Theoretical curves of OC—M—CO bond angle in M(CO)3 groups with approximate trigonal symmetry, with transition metal M enneacoyalent (u = 9) or octacovalent (< = 8), as functions of the bond number n from n = 1 (single bond from metal to carbonyl) to n = 2 (double bond). 

With eight outer electrons in the formally neutral atom, iron needs to acquire an electron to achieve covalence. Often the ninth electron is obtained from a carbonyl group forming a dative single covalent bond, Fe —CO+. The Fe(CO)3 group then involves five of the nine bonds formed by the iron atom, the bond number of the iron-carbonyl bonds being 1.67, and the iron atom forms four other bonds. If the added electron... 

There is also some contribution of structures in which two M—C bonds are broien, with formation of a ring double bond and an unshared electron pair on the metal atom, with no electron transfer. These structures increase the bond number of the carbon-carbon bonds and decrease that of the metal-carbon bonds. 

It is interesting to note that there are strings of tungsten atoms WII in the A15 crystals with each atom between two very near neighbors the interatomic distance 2.519 A. leads to the bond number n = 1.35. 

Zinc crystallizes in a deformed A3 structure with large axial ratio, causing the six equatorial neighbors (at 2.660 A.) to be nearer than the six neighbors in adjacent planes (at 2.907 A.). The bond numbers are 0.54 and 0.21, respectively, leading to 72(1) = 1.249 A. 

In applying the metallic radii in the discussion of the structure of a metal or intermetallic compound either the observed distances may be used with the single-bond radii to calculate the bond numbers, the sums of which may then be compared with the expected valences, or the distances may be compared with the sums of radii for suitable coordination numbers, such as CN12. The correction to be added to i (CN12) to give the radius for another coordination number, the va-... 

Indeed, if the bond numbers are calculated from the observed distances, the following results are obtained... 

The calculated Fe-C distance is 0.03 A. larger than that observed, and the average Fe-Fe distance, 2.57 A., is 0.03 A. smaller than the observed average. It is not unreasonable to expect the same deformation (with opposite sign) for each of six Fe-C bonds as for the opposing seventeen much weaker Fe-Fe bonds (the bond numbers... 

An equation has been formulated to express the change in covalent radius (metallic radius) of an atom with change in bond number (or in coordination number, if the valence remains constant), the stabilizing (bond-shortening) effect of the resonance of shared-electron-pair bonds among alternative positions being also taken into consideration. This equation has been applied to the empirical interatomic-distance data for the elementary metals to obtain a nearly complete set of single-bond radii. These radii have been compared with the normal covalent... 

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